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Your question is vague and has several questions rolled into one. I'll answer them one by one but I would strongly recommend doing some reading on best practices of E-commerce checkout design.

Passing it on to Paypal and let Paypal do all the work : This would be a bad idea since not all your potential users might use Paypal. You must provide multiple ways of payment for your users and just providing one can prove to be a major deterrant and drop off point for your users. To quote this article on Best practices for E-commerce design

Work in steps : This has its advantages and disadvantages. If your steps are linear and well laid out and ensure a seamless experience, you can hope and work against a low drop off rate. However if you have a large number of steps or steps within steps , you could potentially frustrate users with the number of steps they need to perform to do a simple checkout and lose customers. To quote the article Fundamental Guidelines Of E-Commerce Checkout Design

Having steps within steps confuses and intimidates customers as it
breaks with their mental model of a linear checkout. One of the worst
usability violations that we discovered in our testing was non-linear
checkout processes. Websites with a non-linear checkout process left
several of our test subjects confused and intimidated. At the time of
testing, both Walmart and Zappos had a non-linear checkout process.
The typical way to “accidentally” end up with a non-linear checkout
process is to create steps within steps. This happens, for example,
when the customer has to set a “Preferred shipping address” (Walmart’s
violation) or “Create an account” (Zappos’ violation) on a separate
page, and is then redirected to a previous checkout step upon
completion. Below, you can see Walmart’s checkout flow in thumbnails
(click image for larger view). Notice that it’s non-linear because the
“Preferred shipping address” sub-step directs the user to a previous
step:
Blockquote

With regards to your last few questions about the order of extracting information from users,you really should do some self research on UX best practices for E-commerce checkout design. There is no right answer and you have to see what works best for you and what industry best practices show the best conversion rates to ensure you get answers to your questions.